| Line 15: | Line 15: | ||
== Linear classification Problem Statement== | == Linear classification Problem Statement== | ||
| − | In a linear classification problem, the feature space can be divided into different regions by hyperplanes. In this lecture, we will take a two-catagory case to illustrate. Given training samples <math> \vec{y}_1,\vec{y}_2,...\vec{y}_n \in \mathbb{R}^p</math>, each <math> \vec{y}_i </math> is a p-dimensional vector and belongs to either class <math> w_1</math> or <math>w_2</math>. The goal is to find the maximum-margin hyperplane that separate the points | + | In a linear classification problem, the feature space can be divided into different regions by hyperplanes. In this lecture, we will take a two-catagory case to illustrate. Given training samples <math> \vec{y}_1,\vec{y}_2,...\vec{y}_n \in \mathbb{R}^p</math>, each <math> \vec{y}_i </math> is a p-dimensional vector and belongs to either class <math> w_1</math> or <math>w_2</math>. The goal is to find the maximum-margin hyperplane that separate the points in the feature space that belong to class <math>w_1</math> from those belong to class<math>w_2</math>. The discriminate function can be written as |
| + | <math> g(\vec{y}) = c\cdot\vec{y}</math> | ||
. The separation hyperplane can be written as | . The separation hyperplane can be written as | ||
<math> c\cdot y=b </math> | <math> c\cdot y=b </math> | ||
where <math>\cdot </math> denotes the dot product, c determines the orientation of the hyperplane and | where <math>\cdot </math> denotes the dot product, c determines the orientation of the hyperplane and | ||
Revision as of 10:31, 1 May 2014
'Support Vector Machine and its Applications in Classification Problems
A slecture by Xing Liu
Partially based on the ECE662 Spring 2014 lecture material of Prof. Mireille Boutin.
Outline of the slecture
- Linear discriminant functions
- Summary
- References
Linear classification Problem Statement
In a linear classification problem, the feature space can be divided into different regions by hyperplanes. In this lecture, we will take a two-catagory case to illustrate. Given training samples $ \vec{y}_1,\vec{y}_2,...\vec{y}_n \in \mathbb{R}^p $, each $ \vec{y}_i $ is a p-dimensional vector and belongs to either class $ w_1 $ or $ w_2 $. The goal is to find the maximum-margin hyperplane that separate the points in the feature space that belong to class $ w_1 $ from those belong to class$ w_2 $. The discriminate function can be written as $ g(\vec{y}) = c\cdot\vec{y} $
. The separation hyperplane can be written as $ c\cdot y=b $ where $ \cdot $ denotes the dot product, c determines the orientation of the hyperplane and
